24-Ruby IV

Solved

Leo Tolstoy and Mathcad

Forum|Forum|5 years ago
January 12, 2021
6 replies
11036 views

"The race course was a large three-mile ring of the form of an ellipse...".

Anna Karenina, by Leo Tolstoy Translated by Constance Garnett

In Russian text not three-mile, but 4 versta (верста). Versta = 500 Sagen (сажень), Sagen = 7 feets.

The problem.

The workers marked this racetrack like that. They took a rope and tied it with both ends to two pegs driven into the ground and spaced one versta (see above) from each other. Then they pulled this rope and drew an ellipse. How long was this rope? What is the canonic formula of this ellipse?
Who will give the best solution?

Algebra_Geometry

Best answer by ValeryOchkov

For Express- not 3 but one equation

W

Werner_E

25-Diamond I

Guess you know that you can't expect a symbolic solution, do you?

Quite a long rope for the time

V

ValeryOchkov

Author

24-Ruby IV

Thanks, Werner!

One more from Anna Karenina

"- Самолюбия, - сказал Левин, задетый за живое словами брата, - я не понимаю. Когда бы в университете мне сказали, что другие понимают интегральное вычисление, а я не понимаю, - тут самолюбие."

“Self-respect!” said Levin, stung to the quick by his brother’s words; “I don’t understand. If they’d told me at college that other people understood the integral calculus, and I didn’t, then pride would have come in.

Sorry, I know more nice solution.

PS

One interesting article about math and not Leo Tolstoy but Fedor Dostoyevsky

Dostoyevsky as mathematician (part II) | SpringerLink

A

AlanStevens

19-Tanzanite

Here's a more long-winded approach than Werner's. It produces a slightly different result.

A

AlanStevens

19-Tanzanite

Hmm. I tried to post another solution, but had an email saying it was rejected by a moderator. Any idea why? (It contained a jpg image).

I'll try just attaching the (M15) file instead.

My approach was more long-winded than Werner's and produced a slightly different result.

Alan

1_versta.zip

W

Werner_E

25-Diamond I

Are you sure about the formula for the arc length?

Shouldn't it be rather that way:

The difference to my result is now about 1.7*10^-6 % which seems acceptable to me.

Because the Integral uses the derivative of a solve block function, calculation is very slow and a lot of numeric round-offs may sum up.

According your post being rejected by a mod. This really should not happen and is quite strange - especially given the fact, that you sure have built a reputation for yourself as a serious and very valuable forum participant over many years. I also thought that only the postings of new members would be under moderation anyway.

Maybe @Jaime_Lee can shed some light on this.

P.S.: Its nice to see you being around here again!

A

AlanStevens

19-Tanzanite

Thanks Werner, you might be right about the distance, I did it rather quickly, without too much thought - I'll think on it more deeply!

I still look at the site from time to time, but it seems there are more and more PRIME related questions. Since I don't have PRIME I take little interest in them!

Alan